Mathematics – Algebraic Geometry
Scientific paper
2001-06-25
Mathematics
Algebraic Geometry
36 pages
Scientific paper
The cherry on top of this stacky paper is the following: for any g>1 we give a finite group G such that the moduli space of connected admissible G-covers of genus g is a smooth, fine moduli space, which is a Galois cover of the moduli space of stable curves. The proof relies on methods introduced by Looijenga and Pikaart-De Jong, and on the theory of twisted G-covers, a theory announced without proofs in math.AG/9811059, section 3, and developed in the first few sections of this paper. This includes a moduli description of the normalization of the Harris-Mumford space of admissible covers, and a study of moduli of stable curves with abelian and non-abelian level structure.
Abramovich Dan
Corti Alessio
Vistoli Angelo
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